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Full text of "Mathematical And Physical Papers - Iii"

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The effect of friction on the intensity of sound depends on the first power of /. In the case of an indefinite succession of plane waves, it appears that during the time t the amplitude of vibration is diminished in the ratio of 1 to 6~ct, and therefore the intensity in the ratio of 1 to e~2ci, where
Putting X = 1 and t = 1 we get 1 to 0-4923, or 2 to 1 nearly, for the ratio in which the intensity is altered during one second in the case of a series of waves an inch long. The rate of diminution decreases very rapidly as the length of wave increases, so that in the case of a series of waves one foot long the intensity is altered in one second in the ratio of 1 to 0'995095, or 201 to 200 nearly. It appears then that in all ordinary cases the diminution of intensity due to friction may be neglected in comparison with the diminution due to divergence. If we had any accurate mode of measuring the intensity of sound it might perhaps be just possible, in the case of shrill sounds, to detect the effect of internal friction in causing a more rapid diminution of intensity than would correspond to the increase of distance from the centre of divergence.
SECTION II. Suggestions with reference to future experiments
80. I am well aware that the mere proposal of experiments does not generally form a subject fit to be brought before the notice of a scientific society. Nevertheless, as it frequently happens in the division of labour that one person attends more to the theoretical, another to the experimental investigation <>f some branch of science, it is not always useless for the theorist, (,o point out the nature of the information which it would bo most important to obtain from experiment. I hope, therefore, tlmfc I may 1m permitted to offer a few hints with reference to experiments in which the theory of the internal friction of fluids is <:oii<;<>ni<*l. I shall omit all details, since they would properly conic in connexion with the experiments.